膨 rarely stands alone in modern Chinese — it almost always pairs into 膨胀 (péngzhàng, 'to expand/inflate', literal and economic) or 膨大 (péngdà, 'to bulge'). Learn the compounds first; the bare character mostly appears in technical or older writing.
memory
The radical 月 (here standing for 肉, 'flesh') hints at the original sense — flesh that is 'puffed up'. Compare 胀 zhàng (also 月-radical) which is its frequent partner in 膨胀.
Left-side meat radical — the side form of 肉, visually identical to 月 (moon) but historically a slab of striated flesh. Carries the meaning here: 膨 originally described the body distending — a swollen belly, bloated tissue — before extending to any expansion (膨胀 to inflate, 膨大 to balloon).
Right side 彭 supplies the sound — péng stays péng with no shift. 彭 itself once depicted a beaten drum with sound rays flying off, and that sense of resonant bulging echoes the swelling meaning. Same phonetic family: 澎 (in 澎湃 surging waves), 蓬 leafy and abundant.
